SOLUTION: if a person rolls doubles when tossing two dice, the roller profits $95. If the game is fair, how much should the person pay to play the game?

Question 624879: if a person rolls doubles when tossing two dice, the roller profits $95. If the game is fair, how much should the person pay to play the game?
Answer by Edwin McCravy(20055) (Show Source): You can put this solution on YOUR website!
if a person rolls doubles when tossing two dice, the roller profits $95. If the game is fair, how much should the person pay to play the game?

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⚃⚀   ⚃⚁   ⚃⚂   ⚃⚃   ⚃⚄  ⚃⚅

⚄⚀   ⚄⚁   ⚄⚂   ⚄⚃   ⚄⚄  ⚄⚅

⚅⚀   ⚅⚁   ⚅⚂   ⚅⚃   ⚅⚄  ⚅⚅

The probability of wnning (rolling doubles) is 6 out of 36 or . 
The probability of losing is 1- = .

Let $N be the price to pay to make the game fair:

Possible      Probability 
 Outomes      of outcome      Expectation
------------------------------------------
    x               p             xp
------------------------------------------
   $95             1/6            95/6  
   -$N             5/6           -5N/6
-------------------------------------------
                         ∑xp = 

 To make the game fair we set that = 0

              ∑xp =  = 0

                     = 0

Multiply through by 6

                    95 - 5N = 0
                        -5N = -95
                          N = 19

So he should pay $19 to play to make the game fair.

Edwin

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